Shakhtar were unlucky not to get an away goal of their own early on when Roma's Alessandro Florenzi nearly headed an in-swinging free-kick into his own net with a glancing clearance. "We deserve to go through, to be in the quarter-finals".
It took Dzeko just 22 seconds to work Andriy Pyatov for the first time, but Shakhtar would not bow easily to the hosts' early pressure and were soon knocking the ball around with confidence in the Roma half.
Kolarov then crucially swept the ball away from Ferreyra's toe inside the Roma box as the sides went in level at the break.
Dzeko, who had his first chance in the opening minute, broke Shakhtar's stout back four in the 52nd.
Kevin Strootman sent an imposing ball through to the ex-Man City star, who then effortlessly knocked the strike past the keeper.
Trump Tariffs Not Such a Big Deal for Economic Growth
The steel sector , for example, supported as many as 650,000 American workers in the 1950s , yet now employs only about 140,000 . Sinopec, a large state-owned petrochemical company, is said to raise its imports of USA crude oil by 80 per cent this year.
Despite being a man down Shakhtar pushed forward in search of the goal that would send them into the quarterfinals of the competition but they were unable to do so, losing 1-0 on the night and exiting the Champions League on the away goals after a 2-2 aggregate scoreline.
With just 10 minutes remaining a ball boy on the side of the pitch held onto the ball a little too long for the 26-year-old's liking.
"We made a few too many mistakes in the first leg and they made the majority".
The sides have met five times in the Champions League before, with Shakhtar winning on five occasions.
The Giallorossi have played four home games in the Champions League this season against Atletico Madrid, Chelsea, Qarabag and Shakhtar Donetsk without conceding.
However, it was a great campaign for the Ukrainian champions and many of you will be looking forward to seeing them in the UEFA Champions League again next season. Ordets pulled Dzeko back with the striker racing through on goal.